Question

A tree makes a shadow that is 14 ft long. Rachel is 6 ft tall. When she is standing near the tree, her shadow is 3.5 ft long. Which statement BEST explains why Rachel can use a proportion to estimate the length of the tree? A) The triangles made by the tree and its shadow and Rachel and her shadow are similar. B) The triangles made by the tree and its shadow and Rachel and her shadow are adjacent. C) The triangles made by the tree and its shadow and Rachel and her shadow are congruent. D) The triangles made by the tree and its shadow and Rachel and her shadow are symmetric.

Answer 1

The answer would be A) The triangles made by the tree and its shadow and Rachel and her shadow are similar because they are not the same height so they are not congruent or symmetric

Answer 2

Answer: A) The triangles made by the tree and its shadow and Rachel and her shadow are similar.

Explanation:

Since both the tree and the girl is standing vertical to the ground making right angle .

If we assume that the given measure took at same time, then the angle made by sun rays would be same for tree and Rachel. [Corresponding angles]

Thus triangles made by both of them are similar.

Since, the corresponding sides of similar triangles are proportional.

Therefore, the statement BEST explains the reason that Rachel can use a proportion to estimate the length of the tree :-

A) The triangles made by the tree and its shadow and Rachel and her shadow are similar.